Self-similarity of topology in the Internet

Abstract

During the last decade, significant effort have been made toward improving our understanding of the topological structures in complex networks. The dominant theme of these efforts has been on studying the graph-theoretic properties of the corresponding connectivity structures. In this thesis, we presented our research on the graph-theoretic properties of the Internet topology. We first introduced the complex networks, the Internet and their topological properties. Methods and models that are commonly used in the study of complex networks were given in detail. After explaining the concepts of self-similarity and the testing methodology in Internet topology, we found that the self-similarity property exists in both ASlevel and router-level Internet topology. We constructed our Internet topologies on both AS-level and router-level based on the data obtained from topology measurements. By coarse-graining the network topology into different stages of aggregate networks, we observed that both AS-level and router-level Internet topology were scale-invariant in terms of several important network metrics. These results demonstrated that Internet topologies are self-similar at both AS-level and router-level. These suggested that when studying the Internet topology, it is possible to predict the behavior of the Internet with the understandings obtained from its smaller aggregated networks. By comparing the coarse-graining results of several popular topology generators, we found that topologies constructed from two popular models which do not have hierarchical structures were not self-similar. While the topology generated from a model with a hierarchical structure will give rise to self-similarity. This implied that hierarchical structure could be one of the pre-conditions of the self-similarity property in network topology.